Smoothly connect two objects (Cylinder+Plane)
TOPOLOGY

It's always better to work with simple topology, so you don't fall into a troubles with next step in modelling. So I would recommend ...


ad Cylinder 6 sides and Cylinder 12 sides, position them and use Boolean Modifier > Union






to get a same amount of vertices, select loop of hexagon, Subdivide (W) it, select both parts of top surface and delete them, select both loops and search for Bridge





version BEVEL


now you can select loop to Bevel (cmd+B), under Adjust last operation (F9) choose Percentage and set 100%





version BRIDGE


instead of beveling you can select subdivided hexagon edge directly and circle and search Bridge, adjust setup again under Adjust last operation (F9) like seen on screen





For any version - SMOOTH surface


smoothing surface - Subdivision surface Modifier, to sharp edges select them and set Creas (Shift+E) = 1, Set Smooth shading and under Object Data properties > Normals > enable Auto Smooth with Angle like 13 (in this case)





to model hole (tube) you can anytime in a process a) delete face and use Solidify Modifier or b) select face Extrude (E) Scale (S) to make thickness of pipe and extrude again with move inside (before extrude change Transform Orientation > Normals)